Outlier-robust Autocovariance Least Square Estimation via Iteratively Reweighted Least Square

2026-03-09

AI Summary

This work addresses the challenge of accurately estimating process and measurement noise covariances in Kalman filtering when measurements are corrupted by outliers. The standard autocovariance least-squares (ALS) method is highly sensitive to such anomalies, leading to biased covariance estimates. To overcome this limitation, the authors propose a robust ALS-IRLS algorithm that integrates an innovation-based adaptive thresholding mechanism with a Huber cost function derived from an ε-contamination model. This two-stage strategy first identifies and removes anomalous innovations via adaptive thresholding, then refines the covariance estimates through iteratively reweighted least squares. Experimental results demonstrate that the proposed method reduces the root-mean-square error (RMSE) of noise covariance estimation by more than two orders of magnitude compared to standard ALS, achieving state estimation accuracy approaching the ideal Oracle Cramér–Rao lower bound and significantly outperforming existing robust Kalman filtering approaches.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Adversarial Learning & Robustness
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The autocovariance least squares (ALS) method is a computationally efficient approach for estimating noise covariances in Kalman filters without requiring specific noise models. However, conventional ALS and its variants rely on the classic least mean squares (LMS) criterion, making them highly sensitive to measurement outliers and prone to severe performance degradation. To overcome this limitation, this paper proposes a novel outlier-robust ALS algorithm, termed ALS-IRLS, based on the iteratively reweighted least squares (IRLS) framework. Specifically, the proposed approach introduces a two-tier robustification strategy. First, an innovation-level adaptive thresholding mechanism is employed to filter out heavily contaminated data. Second, the outlier-contaminated autocovariance is formulated using an $\epsilon$-contamination model, where the standard LMS criterion is replaced by the Huber cost function. The IRLS method is then utilized to iteratively adjust data weights based on estimation deviations, effectively mitigating the influence of residual outliers. Comparative simulations demonstrate that ALS-IRLS reduces the root-mean-square error (RMSE) of noise covariance estimates by over two orders of magnitude compared to standard ALS. Furthermore, it significantly enhances downstream state estimation accuracy, outperforming existing outlier-robust Kalman filters and achieving performance nearly equivalent to the ideal Oracle lower bound in the presence of noisy and anomalous data.

Problem

• outlier-robust
• autocovariance least squares
• Kalman filter
• noise covariance estimation
• measurement outliers

Innovation

• Autocovariance Least Squares
• Iteratively Reweighted Least Squares
• Outlier-Robust Estimation
• Huber Cost Function
• Kalman Filter